 Welcome to Practical Trigonometry. It would be a lot easier to learn trigonometry if you knew how it was used in the shop. The following problems show some typical trigonometry applications. For simplicity, all length measurements given are in inches. How deep should you feed an 82-degree countersink to get a 0.836-inch diameter hole at the top? To figure out what you know, draw and mark a diagram as shown. Once you know your measurements, label the sides of the triangle according to the angle you are using. In this example, use the formula tangent of the angle equals the opposite side length divided by the adjacent side length. Use algebra to rearrange the terms of the equation and solve as shown. So you would have to feed the countersink 0.481-inches deep to get a diameter of 0.836-inches at the top. Now, try your hand at the following problems. Round your answers to three decimal places. Pause the video while you solve each problem. How deep should you feed a 90-degree countersink to get a 0.458-inch diameter hole at the top? Now watch as the problem is solved. The two legs of a 45-degree triangle are equal, so 0.229-inches is the depth. Note, if you use tangent, as in the example, you should get the same result. This is a shortcut for 45-degree right triangles. What is the width at the bottom of the dovetail? Watch as we solve for the adjacent side. Remember to add it to both sides of the 1-inch length as shown. So the total width is 1.289-inches. How deep does the tip of a 3-eighths-inch drill extend in the hole? Watch the solution for the adjacent side. So the tip of the drill extends 0.113-inches into the hole. What is the included angle of the taper shown at the left? Watch as we solve for the angle. Remember to get the angle, press second, then tan on your calculator to use arc tangent. We need to add both angles together, so double the answer to get 3.950-degrees, or 3-degrees, 57 minutes, 1 second. What is the included angle of the part shown at the left? Watch as we solve for the missing angle. The full angle is 126-degrees, 3 minutes, 58 seconds, or 126.066-degrees. This completes this video, Practical Trigonometry.